Changes

===The uncertainty principle===

===The uncertainty principle===

As a result of the wave nature of a particle, neither position nor [[momentum]] of a particle can never be precisely known.  Whenever its position is measured more accurately (beyond a certain limit), its momentum becomes less certain, and visa versa.  Hence, there is an inherent uncertainty that prevents precisely measuring both the position and the momentum simultaneously. This is known as the [[Heisenberg Uncertainty Principle]]<ref>http://hyperphysics.phy-astr.gsu.edu/Hbase/uncer.html</ref>:

As a result of the wave nature of a particle, certain paired physical properties such as position and [[momentum]] cannot both be precisely known.  Whenever its position is measured more accurately (beyond a certain limit), its momentum becomes less certain, and visa versa.  Hence, there is an inherent uncertainty that prevents precisely measuring both the position and the momentum simultaneously. This is known as the [[Heisenberg Uncertainty Principle]]<ref>http://hyperphysics.phy-astr.gsu.edu/Hbase/uncer.html</ref>:

:<math> Dx \times Dp \ge \frac{h}{4\pi}</math>

:<math> Dx \times Dp \ge \frac{h}{4\pi}</math>